Engineering topics
Publications and source records attributed to Erwin, Daniel A..
The direct Monte Carlo method is used to simulate the transient motion of a confined rarefied gas as a container wall is rapidly heated or cooled. Results show that, for the rapid wall temperature changes, the gas response is better measured by an acoustic, rather than conduction, timescale, with steady state conditions being achieved after about ten wave crossing times.
A hybrid numerical technique previously developed for one-dimensional rarefied gas flows is generalized to two dimensions. The method is based on the fact that the flowfield that develops near a body in a rarefied gas typically contains local regions of continuum, transitional and free-molecular flow. By utilizing the solution technique most appropriate for each region and coupling the techniques in an interface region where both are applicable, more computationally efficient solutions can be obtained, or equivalently, more complex flowfields can be analyzed. The present method combines finite difference solution of the Navier-Stokes equations in the continuum regions, with Direct Simulation Monte Carlo in the more rarefied regions. The two schemes are coupled interactively via a general conservative flux boundary condition. The method is tested by application to the model problem of pressure-driven rarefied flow through a slit. Results show the hybrid scheme offers a speedup of a factor of nearly two for the nominal conditions considered, due to the decrease in the size of the Direct Simulation domain.
Numerical experiments have been performed on normal shock waves with Monte Carlo Direct Simulations (MCDS's) to investigate the validity of continuum theories at very low Mach numbers. Results from the Navier-Stokes and the Burnett equations are compared to MCDS's for both hard-sphere and Maxwell gases. It is found that the maximum-slope shock thicknesses are described equally well (within the MCDS computational scatter) by either of the continuum formulations for Mach numbers smaller than about 1.2. For Mach numbers greater that 1.2, the Burnett predictions are more accurate than the Navier-Stokes results. Temperature-density profile separations are best described by the Burnett equations for Mach numbers greater than about 1.3. At lower Mach numbers the MCDS scatter is too great to differentiate between the two continuum theories. For all Mach numbers above one, the shock shapes are more accurately described by the Burnett equations.
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One-dimensional shock wave properties in helium and argon are predicted using Monte Carlo direct simulation. The collision model is based directly on the interatomic potential taking angular scattering into account. The potential is assumed to be of the Maitland-Smith n(r)-6 form. The detailed validity of the simulation is studied by comparing the predicted macroscopic and miroscopic flow properties in shock waves to a wide range of available data.
Several aspects of the kinetic models used in the collision phase of Monte Carlo direct simulations have been studied. Accurate molecular velocity distribution function predictions require a significantly increased number of computational cells in one maximum slope shock thickness, compared to predictions of macroscopic properties. The shape of the highly repulsive portion of the interatomic potential for argon is not well modeled by conventional interatomic potentials; this portion of the potential controls high Mach number shock thickness predictions, indicating that the specification of the energetic repulsive portion of interatomic or intermolecular potentials must be chosen with care for correct modeling of nonequilibrium flows at high temperatures. It has been shown for inverse power potentials that the assumption of variable hard sphere scattering provides accurate predictions of the macroscopic properties in shock waves, by comparison with simulations in which differential scattering is employed in the collision phase. On the other hand, velocity distribution functions are not well predicted by the variable hard sphere scattering model for softer potentials at higher Mach numbers.
Shock wave thickness predictions from Monte Carlo Direct Simulations, using differential scattering and the Maitland-Smith-Aziz interatomic potential, underpredict experiments as shock Mach numbers increase above about 4. Examination of several sources of data has indicated that at relatively high energies the repulsive portion of accepted potentials such as the Maitland-Smith-Aziz may be too steep. An Exponential-6 potential due to Ross, based on high energy molecular beam scattering data and shock velocity measurements in liquid argon, has been combined with the lower energy portion of the Maitland-Smith-Aziz potential. When this hybrid potential is used in Monte Carlo Direct Simulations, agreement with experiments is improved over the previous predictions using the pure Maitland-Smith-Aziz form.
The structure of normal shock waves in binary mixtures is analyzed, using Monte Carlo direct simulation, and compared with previous experimental data. Previous work by Erwin et al. used a collision method based directly on the intermolecular potential function; the present work extends this approach to binary mixtures, obtaining heteromolecular collision cross sections from the corresponding potentials. Results are presented for helium-argon mixtures, with conditions corresponding to the experiments of Harnett and Muntz (1972).
The flow velocity of atomic hydrogen in the plume of an ammonia-propelled arcjet was measured using LIF. The velocity was obtained by the Doppler shift of the absorption peak of the Balmer alpha spectral line. Measurements were made at the nozzle exit, varying the distance from the plume centerline. Results are presented for arcjet operating conditions 13, 20 and 27 kW with a mass flow of 0.31 g/s. The on-axis H flow velocity varies from 14 km/s to 28 km/s over this range of input power. The axial velocity as a function of the distance from the axis is sharply peaked, dropping to almost zero at a radius of less than 5 mm.
The use of high-current short-pulse electron beams in low-density gas flow diagnostics is introduced. Efficient beam propagation is demonstrated for pressure up to 300 microns. The beams, generated by low-pressure pseudospark discharges in helium, provide extremely high fluorescence levels, allowing time-resolved visualization in high-background environments. The fluorescence signal frequency is species-dependent, allowing instantaneous visualization of mixing flowfields.
Velocity distribution functions in normal shock waves in argon and helium are calculated using Monte Carlo direct simulation. These are compared with experimental results for argon at M = 7.18 and for helium at M = 1.59 and 20. For both argon and helium, the variable-hard-sphere (VHS) model is used for the elastic scattering cross section, with the velocity dependence derived from a viscosity-temperature power-law relationship in the way normally used by Bird (1976).
A general theory of stopping power for electrons and ions in a target medium (gas, liquid, or thin solid foil) containing neutral as well as positive and negative ions is developed. The approach is quite accurate in the low- and medium-energy range (less than 1 MeV), where the Bethe stopping-power cross section is inaccurate. The energy transfer during individual collisions is treated by the binary-encounter approximation. The theory is applied to determine the stopping power of seawater, whose major components are H2O molecules and Na(+) and Cl(-) ions. The stopping-power cross sections for low- and medium-energy protons in water show excellent agreement with existing measurements.